1. Field of the Invention
The present invention relates to a pattern forming method, and more particularly to a pattern forming method for forming a pattern by arranging elementary pattern marks which are elements of pattern formation.
The term pattern as herein used includes picture representation as well as character, pattern and graphic representation; the term elementary pattern marks herein used means the minimum units of printed marks to draw a pattern, for example, those corresponding to record dots on a recording medium in dot recording. By way of example, when one picture element or cell (pixcel) is formed by one elementary pattern mark, the elementary pattern mark and the picture cell correspond to each other, but when one picture cell is formed by a plurality of elementary pattern marks, the elementary pattern marks and the picture cell must be recognized differently.
The present invention also relates to an image forming apparatus for forming an image by elementary pattern marks, and more particularly to an image forming apparatus capable of reproducing a high tonality or gradient of image.
2. Description of the Prior Art
In ink dot recording for recording a pattern such as a picture by forming ink dots on a record medium (e.g. record paper) by discharging colored ink droplets, it has been proposed to selectively use inks of different color densities (optical densities) (for respective colors in case of color recording) in order to reproduce a high tonality of image.
When a television image is to be recorded by the ink dot recording which selectively uses the inks of different color densities in order to reproduce the high tonality of image, it is possible to reproduce the image by small diameter dots of high density ink and large diameter dots of low density ink under a given dot pitch for a prepresentation of an image portion of a certain average optical reflection density (if the high and low density inks are used). However, even if the average optical reflection densities of those inks are substantially equal, a resulting printed image appears substantially different in image quality. Although it depends on the ink density and the dot pitch, the image portion represented by the small diameter dots of the high density ink imparts a strong feeling of roughness and it is frequently a significant cause of degradation of the image quality of the image representation.
A theoretical analysis for the above is as follows.
This involves a space-frequency analysis of an image recorded by recording dots of a constant dot pitch and a constant dot diameter with a given color density in a sufficiently wide area on a record medium.
For simplicity, assume a one-dimensional model as shown in FIG. 1. While dots are actually arranged in two dimensions, they may be considered to be one-dimensional on a line passing through centers of the dots when they are viewed in a space-frequency fashion. A brightness distribution is represented by f(x) in FIG. 1, where x represents a positional coordinate on the line and y represents an optical reflection brightness at the position x. A reflection brightness of the record medium (such as paper) is represented by a.sub.0 (optical reflection density: -log a.sub.0), a reflection brightness of the colored dot is represented by a.sub.1 (optical reflection density: -log a.sub.1), a dot radius is represented by b and dot pitch T is represented by T, and a=a.sub.0 -a.sub.1.
Assuming that the dots are arranged in the sufficiently wide area on the record medium, and the number of dots is 2N+1, then a Fourier transform of f(x) is given by ##EQU1##
Assuming that N is sufficiently large, the first term of the formula (1) can be regarded as a delta function. Further, ##EQU2## in the second term can be regarded as a delta function series.
Accordingly, ##EQU3## where .omega..sub.0 =2.pi./T and k is an integer.
F.sub.N (.omega.) when N is sufficiently large is represented by F(.omega.) as follows. ##EQU4## where l is an integer other than zero. An example of a function by the formula (3) is shown in FIG. 2. In addition to a D.C. component at .omega.=0, an impulsative space-angular frequency component at a period of 2.pi./T is included since a relation between .omega. and a space frequency f is given by EQU .omega.=2.pi.f (4)
the impulsative space-frequency component at a period of 1/T appears on a space-frequency axis. The formula (3) is rewritten as follows. ##EQU5## [where f.sub.0 =1/T]
An example of a function of the formula (5) is shown in FIG. 3. By defining a duty factor D as a ratio of a dot diameter 2b to the dot pitch T (see FIG. 1), that is, EQU D=2b/T (6)
then ##EQU6## In the formula (7), the first term represent a D.C. component and it indicates that an average reflection intensity is equal to (a.sub.1 -aD). The second term represent a high frequency component and indicates that it corresponds to a component at a frequency of 1/T when l=1 and assumes the following value. ##EQU7##
When an image is to be represented by forming ink dots at a frequency f.sub.0, a frequency band of an image which can actually be represented by such ink dots is approximately f.sub.0 /2 in accordance with the sampling theory, and components at higher frequencies are regarded as noise. Since the resolution power of the human eye is approximately one minute, the resolution power of a human eye on a record medium at an ordinary viewing distance, that is, at a so-called range of clear vision (25-30 cm) is approximately 10 lp/mm at most. Accordingly, the frequency components in excess of 10 lp/mm can be neglected. Thus, in FIG. 3, assuming that 2f.sub.0 =10 lp/mm, the frequency components at approximately f.sub.0 =5 lp/mm significantly affect the feeling of image quality. Accordingly, it may be considered that a magnitude of a power spectrum F.sup.2 (f.sub.0) at the frequency f.sub.0 significantly affects the feeling of image quality.
From the formula (8), when the duty factor D is changed in a range of 0-1 or larger, the power spectrum F.sup.2 (f.sub.0) at the frequency f.sub.0 is a sine function as shown in FIG. 4, which is maximum at D=0.5 and zero at D=0 and D=1.
Accordingly, when the image is to be represented by the dots, the power spectrum F.sup.2 (f.sub.0) is maximum when the duty factor D is 0.5 and stimulation of the eye by the dot is large. This stimulation gives a feeling of roughness.
Since the power spectrum F.sup.2 (f.sub.0) is represented by EQU F.sup.2 (f.sub.0)=(a/.pi.).sup.2 sin.sup.2 .pi.D (9)
it depends on a difference .alpha. between the reflection brightness of the colored ink dots and the reflection brightness of the record medium. The smaller the difference .alpha. of the reflection brightness is, the smaller is the power spectrum F.sup.2 (f.sub.0). Accordingly, it may be considered that the feeling of image quality is enhanced by using ink of as low color density as possible even when the same average optical density is to be represented. In fact, the power spectrum F.sup.2 (f.sub.0) when the reflection brightness difference .alpha. and the duty factor D are changed such that the first term of the formula (7) (a.sub.1 -aD) is kept constant may be examined.
For example, when a certain average optical density is to be represented by the dots having a duty factor D.sub..alpha. by using ink which causes the reflection brightness of (a.sub.1 -a.sub..alpha.) of the dots on the record medium, it is necessary to satisfy a relation of EQU [a-(a.sub.1 -a.sub..alpha.)D.sub..alpha. ]=constant (10)
From the formula (10), EQU a.sub..alpha. D.sub..alpha. =constant (11)
and the power spectrum F.sup.2 (f.sub.0) is represented by ##EQU8## The formula (12) is a monotonously decreasing function in a range of 0.ltoreq.D.ltoreq.1 as shown in FIG. 5. Thus, the closer to unity the duty factor D is, the smaller is the power spectrum F.sub..alpha..sup.2 (f.sub.0). Thus, in order to represent the same average optical density, a higher image quality is obtained by reducing the difference between the reflection intensities of the dots and the record medium (that is, by using the ink of as low color density as possible) and bringing the duty factor close to unity.
To state it differently, the power spectrum F.sup.2 (f.sub.0) is maximum at D=0.5 as shown in FIG. 6 whether the high density ink is used or the low density ink is used, but the power spectrum F.sup.2 (f.sub.0) when the low density ink is used is larger. Accordingly, it is said from qualitative analysis that the low density ink can better enhance the feeling of image quality. It was proved in an experiment that the roughness was not noticeable at the duty factor D of 0.5 when the low density ink was used but the roughness was noticeable when the high density ink was used. An area having the duty factor D higher than A, which is a minimum value of the power spectrum which causes roughness, noticeably adversely affects the image quality. Accordingly, the smaller the area having the duty factor larger than A is, the better is the quality of the image as a whole.
As to a high frequency component, the same is applicable as shown in FIG. 7.
By way of example, FIG. 6 shows power spectra of patterns formed by dots on a white paper having an optical reflection density of approximately 0.1 (reflection factor: approximately 80%) by using a high density ink selected from inks having ink density of 1-2 (dye or pigment content: approximately 2-5% by weight) and a low density ink selected from inks having ink density of 0.3-0.6 (dye or pigment content: approximately 0.2-0.5% by weight), at a dot space frequency of 5 dots/mm (called the number of pels), that is, at a dot pitch T of 200 .mu.m. In an experiment, when an ink having the ink density of 0.6 (dot reflection factor: 10%) was used the power spectrum F.sup.2 (f.sub.0) at the duty factor D of 0.5 under the same condition (the same number of pels and the same record medium) exceeded A shown in FIG. 6.
The ink density ID is defined by ##EQU9## where I.sub.in is a light intensity irradiated to the ink and I.sub.th is an intensity of transmitted light therefrom. The optical reflection density OD is defined by ##EQU10## where I.sub.i is a light intensity irradiated to a given area and I.sub.0 is an intensity of reflected light therefrom.
While N was assumed to be sufficiently large in the above theoretical analysis, the conclusion may be applicable to a case where N is 1 or larger. The above analysis is based on the relative density of the ink dots to the record medium rather than the absolute density. However, since white paper having a very low optical reflection density (e.g. approximately 0.1) is frequently used as the record medium, the above conclusion is substantially valid when only the absolute density of the ink dots is considered. The characteristic curve shown in FIG. 6 varies in accordance with the dot frequency f.sub.0 or the number of pels, but since the resolution power of the human eye is approximately 10 pels, the feeling of roughness is critical when the number of pels is larger than 10 or the dot pitch is smaller than 100 .mu.m. More specifically, the number of pels of 4-6 is most critical. (The representation of the image is not suitable with the smaller number of pels and the feeling of roughness is relieved with the larger number of pels.)
While the curve in FIG. 6 was depicted for the black ink, a more or less similar tendency is observed for other colors.
While the pattern formation by the ink dots has thus for described, the same is true for electronic photographing, thermal recording (thermal transferring) and electrostatic recording.
In the ink jet printer, the following methods have been proposed to reproduce a high tonality of image.
In a first method, the quantity of liquid discharged from an ink jet head is controlled to vary a diameter of dots printed so that the tonality is represented.
In a second method, the dot diameter is not varied but each picture cell comprises 4.times.4 sub-pixcel matrix, to which a dither method is applied to reproduce the tonality. In the first method, it is difficult practically to attain a wide range of printable dot diameters and only several steps of tonalities can be reproduced. It is therefore insufficient to print out a television image or a photograph image.
The second method resolves the disadvantage of the first method. When one picture cell comprises a 4.times.4-matrix, it is possible to reproduce 17 steps of tonalities. However, a print speed is 1/16 of that of the first results because each picture cell comprises 4.times.4=16 sub-cells, or the number of print heads must be increased by a factor of 16 in order to increase the print speed. However, this results in a complex structure of print heads and a large electric circuit for processing the image by the dizzer method. As a result, a total cost is significantly increased.
The diameter of the dot which can be formed by a certain ink jet head is 70-280 .mu.m. When it is desired to attain the high tonality by varying the dot diameter, a maximum dot diameter of approximately 200 .mu.m-280 .mu.m is required, and when overlapping areas are small, each pixcel comprises 4-6 dots/mm (which is referred to as pels). In a video printer which reproduces an image from a television signal, the number of pixcels is 525.times.(525.times.(4/3)) because the number of scan lines in one frame of the television signal is 525 for the NTSC system. Of those, the number of pixcels in an effective screen area is approximately 480.times.640 dots.
Thus, when each pixel comprises 5 pels, a screen size is 96.times.128 mm which is suitable for viewing in a range of clear vision.
When inks of different color densities are used, smaller dots are to be formed by the ink of higher color density or larger dots are to be formed by the ink of lower color density in order to attain the same average optical reflection density. However, even if the reflection densities are equal, there is a big difference between the feeling of image quality. Specifically, the image represented by the high color density ink imparts feeling of higher roughness than the image represented by the low color density ink, and the image quality of the former is lower.
When a minimum density dot is to be represented by non-print of dot, white areas appear on the printed image. The tone of the white areas is clearly different from the tones of the other dot-printed areas. As a result, the image quality is degraded.
From the above analysis, it is seen that a higher quality of image is obtained as a whole when the high density dots are not used, but the range of tonality attainable by only low density dots is limited.